A new method to retrieve phase information for equiangular fan beam differential phase contrast computed tomography

Sample radiation damage is one of the main drawbacks limiting applications of the x-ray phase-contrast imaging method. Recently, for x-ray grating-based phase contrast imaging, the reverse projection (RP) method has been proposed by Zhu et al. [Proc. Natl. Acad. Sci. U.S.A. 107, 13576-13581 (2010)]. Compared to the conventional phase stepping technique, the RP method allows a strong reduction of the exposure time and minimization of the errors induced by mechanical vibrations. However, so far, it has only been considered for parallel beam illumination, typical of a synchrotron radiation source. In this paper, a generalization of the RP method from parallel beam geometry to fan beam geometry was presented and discussed.Within parallel beam geometry, the RP method utilizes the conjugate characteristic between reverse projection images. Nevertheless, this characteristic is not directly satisfied for fan beam geometry. In this study, a phantom composed of known materials was constructed and the projection images of the phantom were calculated in a fan beam geometry. By considering single ray, the conjugate images of the projection images were derived from the projection dataset. After that, using the modified RP method the authors retrieved phase and absorption information from paired images.Extracted phase and absorption information of the phantom were in good agreement with theoretical values. Additionally, the slice reconstruction was performed and the results turned out to be in the authors' expectation.Theoretical calculations and numerical simulations confirm both feasibility and validity of the RP method under fan beam illumination. Because this method is simple, fast, and releases a relatively low dose, the authors believe that this research is very useful for the x-ray phase contrast imaging applications in clinical diagnosis, bioresearch, and industrial nondestructive testing.